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DISSIpATIVITY AND EXpONENTIAL STABILITY OF θ-METHODS FOR SINGULARLY pERTURBED DELAY DIFFERENTIAL EQUATIONS WITH A BOUNDED LAG

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Journal of Computational mathematics 2003年第6期21卷 715-726页

作者： Hong-jiong Tian (department of mathematics, Shanghai Normal university, Shanghai 200234, China) department of mathematics Shanghai Normal University Shanghai 200234 China

This paper deals with analytic and numerical dissipativity and exponential stability of singularly perturbed delay differential equations with any bounded state-independent lag. Sufficient conditions will be presented to ensure that any solution of the singularly perturbed delay differential equations (DDEs) with a bounded lag is dissipative and exponentially stable uniformly for sufficiently small ε > 0. We will study the numerical solution defined by the linear θ-method and one-leg method and show that they are dissipative and exponentially stable uniformly for sufficiently small ε > 0 if and only if θ = 1.

关键词： Singular perturbation θ-methods Dissipativity Exponential stability.

Latent ancestral graph of structure vector autoregressive models

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Journal of Systems Engineering and Electronics 2010年第2期21卷 233-238页

作者： Wei Gao1,2and Zheng Tian2,3 1.School of Statistics,Xi’an university of Finance&Economics,Xi’an 710061,p.R.China 2.department of Applied mathematics,Northwestern polytechnical university,Xi’an 710072,p.R.China 3.State Key Laboratory of Remote Sensing Science,Institute of Remote Sensing Applications,Chinese Academy of Sciences,Beijing 100101,p.R.China School of Statistics Xi'an University of Finance & EconomicsXi'an 710061P.R.China department of Applied mathematics Northwestern Polytechnical UniversityXi'an 710072P.R.China department of Applied mathematics Northwestern Polytechnical UniversityXi'an 710072P.R.China State Key Laboratory of Remote Sensing Science Institute of Remote Sensing ApplicationsChinese Academy of SciencesBeijing 100101P.R.China

A class of latent ancestral graph for modelling the dependence structure of structural vector autoregressive （VAR） model affected by latent variables is proposed. The graphs are mixed graphs with possibly two kind of edges, namely directed and bidirected edges. The vertex set denotes random variables at dif- ferent times. In Gaussian case, the latent ancestral graph leads to a simple parameterization model. A modified iterative conditional fitting algorithm is presented to obtain maximum likelihood esti- mation of the parameters. Furthermore, a log-likelihood criterion is used to select the most appropriate models. Simulations are performed using illustrative examples and results are provided to demonstrate the validity of the methods.

关键词： multivariate time series latent ancestral graph itera- tive conditional fitting.

The principal Eigenvalue for Jump processes

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Acta Mathematica Sinica,English Series 2000年第3期16卷 361-368页

作者： Mufa Chen department of mathematics,Beijing Normal university,Beijing 100875,p.R.China department of mathematics Beijing Normal University Beijing 100875 P. R. China

A variational formula for the lower bound of the principal eigenvalue of general Markov jump processes is *** result is complete in the sense that the condition is fulfilled and the resulting bound is sharp for Markov... 详细信息

关键词： principal eigenvalue Jump processes Variational formula for Dirichlet form

Normality and shared values concerning differential polynomials

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Science China mathematics 2010年第3期53卷 749-754页

作者： LEI ChunLin 1 & FANG MingLiang 2, 1 department of Applied mathematics, South China Agricultural university, Guangzhou 510642, China 2 Institute of Applied mathematics, South China Agricultural university, Guangzhou 510642, China 1. department of Applied mathematics South China Agricultural University Guangzhou 510642 China2. Institute of Applied Mathematics South China Agricultural University Guangzhou 510642 China

Let F be a family of functions meromorphic in a domain D, let p be a polynomial with either deg p≥3 or deg p = 2 and p having only one distinct zero, and let b be a finite nonzero complex number. If, each pair of fun... 详细信息

关键词： meromorphic function normality shared value

On the Construction of Regular Orthocryptogroups

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Acta Mathematica Sinica,English Series 2002年第3期18卷 517-530页

作者： Xiang Zhi KONG department of mathematics, Zhengzhou university. Zhengzhou 450052, p. R. China department of mathematics, Qufu Normal university, Qufu 273165. p. R. China department of mathematics Zhengzhou University Zhengzhou P. R. China department of mathematics Qufu Normal University Qufu P. R. China

The aim of this paper is to study regular orthocryptogroups. After obtaining some charac- terizations of such semigroups, we establish the construction theorem of regular orthocryptogroups. As an application, we give the construction theorem of right quasi-normal orthocryptogroups and study homomorphisms between two regular orthocryptogroups.

关键词： Completely regular semigroup Regular band Orthodox Homomorphism Natural partial order

THE INDUCED REpRESENTATION OF C^＊-GROUpOID DYNAMIC SYSTEMS

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Chinese Annals of mathematics,Series B 1996年第1期17卷 103-114页

作者： FANG XIAOCHUN(department of mathematics, Tongji university, Shanghai 200029, China.) TONGJI UNIV DEPT MATHSHANGHAI 200029PEOPLES R CHINA

Let G be a second countable locally compact groupoid with Haar system {λu}, H be a closed subgroupoid containing Go with Haar system {λuH}. *** introduced the C*-Groupoid dynamic system (G, A, α) and its reduced crossed product Cr.d(G, A) in [2], where A is a C*-algebra, α is the homomorphism G→Aut(A). In this paper the author introduces the C*-groupoid dynamic systems (H, A, α|H) and (H\G2, A, α) induced by (G, A, α) and proves that C~*red(H, A) and C~*red(H\G2, A) are strongly Morita equivalent. Moreover the induced representation from C~*red(H, A) to C~*red(G, A) is got.

关键词： C~*-groupoid dynamic system Induced representation Haar system

(1.2)INVERSES OF OpERATORS BETWEEN BANACH SpACES AND LOCAL CONJUGACY THEOREM

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Chinese Annals of mathematics,Series B 1999年第1期20卷 57-62页

作者： MA JIpU(department of mathematics,Nanjing university,Nanjing 210093,China) Nanjing Univ Dept Math Nanjing 210093 Peoples R China

Let E and F be Banach spaces and f non-linear C1 map from E into F. The main result isTheorem 2.2, in which a connection between local conjugacy problem of f at x0E and a localfine property of f'(x) at x0(see the Definition 1.1 in this paper) are obtained. This theoremincludes as special cases the two known theorems: the finite rank theorem and Berger's Theoremfor non-linear Fredholm operators. Moreover, the thcorem gives rise the further results for somenon-linear semi-Fredholm maps and for all non-linear semi-Wedholm maps when E and F areHilbert spaces. Thus Theorem 2.2 not only just unifies the above known theorems but alsoreally generalizes them.

关键词： Nonlinear semi-Fredholm maps Conjugacy problem Banach space

A Series of Soliton-like and Double-like periodic Solutions of a (2+1)-Dimensional Asymmetric Nizhnik-Novikov-Vesselov Equation

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Communications in Theoretical physics 2004年第11期42卷 655-660页

作者： CHEN Yong,~(1,3,4, WANG Qi~(2,4) LI Biao~(2,4) ~1department of mathematics,Ningbo university,Ningbo 315211,China ~2department of Applied mathematics,Dalian university of Technology,Dalian 116024,China ~3department of physics,Shanghai Jiao Tong university,Shanghai 200030,China ~4Key Laboratory of mathematics Mechanization~ the Chinese Academy of Sciences,Beijing 100080,China Key Laboratory of mathematics Mechanization the Chinese Academy of Sciences Beijing 100080 China

We generalize the algebraic method presented by Fan [***.A:***.36 (2003) 7009)] to uniformlyconstruct a series of soliton-like solutions and double-llke periodic solutions for nonlinear partial differential equations(NpDE),As an application of the method,we choose a (2+1)-dimensional asymmetric Nizhnik-Novikov-Vesselov equa-tion and successfully construct new and more general solutions including a series of nontraveling wave and coefficientfunctions’ soliton-like solutions,double-like periodic and trigonometric-like function solutions.

关键词： symbolic computation soliton-like solution Weierstrass and Jacobi elliptic functions periodic solution

ON CLASSIFICATION OF pROJECTIVE VARIETIES WITH NON-INTEGRAL NEF VALUES

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Chinese Annals of mathematics,Series B 2001年第2期22卷 255-262页

作者： ZHAO YICAI department of mathematics, Jinan university, GuangZhou 510632, China. department of mathematics Jinan University Guangzhou 510632 China

Let M be an n-dimensional normal projective variety with only Gorenstein, terminal, Qfactorial singularities. Let L be an ample line bundle on M. Let r denote the nef value of (M, L). The classification of (M, L) via ... 详细信息

关键词： Nef value morphism Ample line bundle projective variety